Theme Essential Question: How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
How do you solve multi-step problems with rational numbers?
How can you solve real-world mathematical problems involving the four operations with rational numbers?
Standards:
7.NS.3: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
Objectives:
The student will solve real-world applications with multiplication and division of rational numbers.
The student will apply properties of operations as strategies to add, subtract, multiply and divide rational numbers.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team Mathematical Practice # 1 asks students to make sense of problems and persevere in solving them. Students must analyze the problem and make conjectures about the form and meaning of the solution. A plan is formed and solutions are checked for making sense. They must use their knowledge of rational number operations along with order of operations to solve problems in this unit.
Students consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. The project at the end of this unit requires students to demonstrate their mastery of the objectives they’ve been taught and practiced during the previous weeks. Students can begin the project, noted below, this week or next. As students work to complete the real-world story problems and the group activity, you should be able to observe implementation of appropriate Mathematical Practices.
Assessment: Product
Student will begin creating two real-world story problems applying the four operations to rational numbers using newspapers and/or magazines as a resource.
Key Questions
How would you explain your strategy (ies) in approaching, developing, and solving real-world and mathematical problems involving the four operations with rational numbers?
Observable Student Behaviors
The student can apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
The student can solve real-world and mathematical problems involving the four operations with rational numbers.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Associative property of multiplication Commutative property of addition
Commutative property of addition Distributive property of multiplication over addition
Identity property of addition Identity property of multiplication Order of operations
Suggested Activities:
Houghton Mifflin OnCore Mathematics Middle School Grade 7 1-6 , p. 23-26
ABC Mastering the Common Core in Mathematics Chapter 3.8 p. 30, 4.7 p.40
Gizmo Lessons
None
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
NS.3 p. 98
Highly Recommended: http://illustrativemathematics.org/illustrations/298 (NS.3) The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 8th GP1 p. 75-134
Glencoe Mathematics Application and Concepts Course 2 pp. 210 – 213, and 244 - 266
Glencoe Pre-Algebra pp. 200 – 219
To solve real-world problems using integers & other rational numbers
Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
http://illuminations.nctm.org/LessonDetail.aspx?id=L849 We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.
Classic Middle-Grades Problems for the Classroom
http://illuminations.nctm.org/LessonDetail.aspx?ID=L264 This lesson presents two classic problems (Mangoes Problem and Sailors and Coconuts) that can be represented and solved in several different ways. Middle-grades students work in groups on the problems to promote communication of mathematical ideas, and a variety of classroom solution attempts are described. This lesson plan was adapted from an article, written by Jerry Stonewater, which appeared in the November‑December 1994 issue of Mathematics Teaching in the Middle School.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257 The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
Grid and Percent It
http://illuminations.nctm.org/LessonDetail.aspx?ID=L249 In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.
Ideas with Food
http://illuminations.nctm.org/LessonDetail.aspx?ID=U78 The following lessons focus on student organization, preparation, and presentation of some simple foods as a way of applying various mathematical concepts, with problem-solving techniques being central to almost all the activities. This unit was adapted from the "Ideas" column in the February 1994 issue of The Arithmetic Teacher, Vol. 41, No. 6, pp. 309.
Learning about Multiplication Using Dynamic Sketches of an Area Model
http://www.nctm.org/standards/content.aspx?id=25090 Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L285 In this lesson, students experience beginning-algebra concepts through discussion, exploration, and videotaping. The concept of multiplication of integers is presented in a format which encourages understanding, not simply rote memorization of facts. This lesson plan is adapted from the article, "A Videotaping Project to Explore the Multiplication of Integers", by Marcia B. Cooke, which appeared in Arithmetic Teacher, Vol. 41, No. 3 (November 1993) pp. 170-171.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699 Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
Real Estate Tycoon
http://illuminations.nctm.org/LessonDetail.aspx?ID=L279 In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School.
Shopping Mall Math
http://illuminations.nctm.org/LessonDetail.aspx?ID=U99 Students participate in activities in which they develop number sense in and around the shopping mall. The first lesson in this unit is appropriate for grades 3 - 5, and the second lesson is appropriate for grades 6 - 8. Both grade-level activities deal with size and space, estimation, measurement, and applications involving percent. This unit was adapted from an article entitled "Mathematics at the Mall," written by Francis Fennell, which appeared in Teaching Children Mathematics, January, 1998, vol.4, no.5, pp. 268 - 274.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252 In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations.
Content: Solving Problems with Rational Numbers
Theme Essential Question:
How can you apply and extend the usage of rational numbers when dealing with real world problems?
Essential Questions:
Standards:
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
Mathematical Practice # 1 asks students to make sense of problems and persevere in solving them. Students must analyze the problem and make conjectures about the form and meaning of the solution. A plan is formed and solutions are checked for making sense. They must use their knowledge of rational number operations along with order of operations to solve problems in this unit.
Students consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution.
The project at the end of this unit requires students to demonstrate their mastery of the objectives they’ve been taught and practiced during the previous weeks. Students can begin the project, noted below, this week or next. As students work to complete the real-world story problems and the group activity, you should be able to observe implementation of appropriate Mathematical Practices.
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Terminating Decimals Repeating Decimals Associative property of addition
Associative property of multiplication Commutative property of addition
Commutative property of addition
Distributive property of multiplication over addition
Identity property of addition
Identity property of multiplication Order of operations
Suggested Activities:
- Houghton Mifflin OnCore Mathematics Middle School Grade 7 1-6 , p. 23-26
- ABC Mastering the Common Core in Mathematics Chapter 3.8 p. 30, 4.7 p.40
- Gizmo Lessons
- None
- Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
- NS.3 p. 98
Highly Recommended:http://illustrativemathematics.org/illustrations/298 (NS.3)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
- JBHM 8th GP1 p. 75-134
- Glencoe Mathematics Application and Concepts Course 2 pp. 210 – 213, and 244 - 266
- Glencoe Pre-Algebra pp. 200 – 219
- To solve real-world problems using integers & other rational numbers
http://www.mathscore.com/math/practice/Integers%20In%20Word%20Problems/- Dividing complex fractions (fractions within fractions)
http://www.sosmath.com/algebra/fraction/frac4/frac4.htDiverse Learners:
Homework:
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts
Literary Texts
- Fractions
http://sci.tamucc.edu/~eyoung/fractions_literature.html- Less Than Zero (MathStart 3) Stuart J. Murphy
Perry the Penguin needs 9 clams to buy an ice scooter -- but he's not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.http://www.amazon.com/exec/obidos/tg/detail/-/0060001267/qid=1088704854/sr=1-2/ref=sr_1_2/002-0537282-1976045?v=glance&s=books
- Mathematics in Children's Literature:
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature BibliographiesMany children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
Sight Words
SMART Board Lessons, Promethean Lessons
Other Activities, etc.
- Big Math and Fries
http://illuminations.nctm.org/LessonDetail.aspx?id=L849We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.
- Classic Middle-Grades Problems for the Classroom
http://illuminations.nctm.org/LessonDetail.aspx?ID=L264This lesson presents two classic problems (Mangoes Problem and Sailors and Coconuts) that can be represented and solved in several different ways. Middle-grades students work in groups on the problems to promote communication of mathematical ideas, and a variety of classroom solution attempts are described. This lesson plan was adapted from an article, written by Jerry Stonewater, which appeared in the November‑December 1994 issue of Mathematics Teaching in the Middle School.
- Elevator Arithmetic
http://illuminations.nctm.org/LessonDetail.aspx?ID=L733Students will use vertical movement of an elevator to evaluate signed number expressions.
- Flipping for Integers
http://illuminations.nctm.org/LessonDetail.aspx?ID=L734In this lesson, students will adapt expressions that add or subtract two signed integers. This lesson builds on the previous lesson in the unit, where students add/subtract just a positive integer from a signed integer.
- Fun with Baseball Stats
http://illuminations.nctm.org/LessonDetail.aspx?ID=L257The following grades 6-8 activities allow students to explore statistics surrounding baseball. They are exposed to connections between various mathematical concepts and see where this mathematics is used in areas with which they are familiar. This lesson plan is adapted from the May 1996 edition of Mathematics Teaching in the Middle School.
- Grid and Percent It
http://illuminations.nctm.org/LessonDetail.aspx?ID=L249In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.
- Ideas with Food
http://illuminations.nctm.org/LessonDetail.aspx?ID=U78The following lessons focus on student organization, preparation, and presentation of some simple foods as a way of applying various mathematical concepts, with problem-solving techniques being central to almost all the activities. This unit was adapted from the "Ideas" column in the February 1994 issue of The Arithmetic Teacher, Vol. 41, No. 6, pp. 309.
- Learning about Multiplication Using Dynamic Sketches of an Area Model
http://www.nctm.org/standards/content.aspx?id=25090Students can learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1 with this tool. Using interactive figures, students can investigate how changing the height of a rectangle with a fixed width changes its area. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
- Magic Squares
http://illuminations.nctm.org/LessonDetail.aspx?ID=L263This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. This lesson is based upon an article from the April 2001 edition of Mathematics Teaching in the Middle School.
- Multiplying Integers Using Videotape
http://illuminations.nctm.org/LessonDetail.aspx?ID=L285In this lesson, students experience beginning-algebra concepts through discussion, exploration, and videotaping. The concept of multiplication of integers is presented in a format which encourages understanding, not simply rote memorization of facts. This lesson plan is adapted from the article, "A Videotaping Project to Explore the Multiplication of Integers", by Marcia B. Cooke, which appeared in Arithmetic Teacher, Vol. 41, No. 3 (November 1993) pp. 170-171.
- Percent Slope Tool
http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-PerSlopeTool.pdfThis reproducible activity, from an Illuminations lesson, provides a template by which students can create a tool for calculating the slope of real-world inclines.
- Power Up
http://illuminations.nctm.org/LessonDetail.aspx?ID=L699Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
- Real Estate Tycoon
http://illuminations.nctm.org/LessonDetail.aspx?ID=L279In this year-long project, students design, "build," and "sell" a house; after which they simulate investment of the profits in the stock market. Along the way, students make scale drawings, compute with fractions and decimals in various contexts, and even solve simple equations. This lesson plan was adapted from an article by David B. Smith, which appeared in the September 2000 edition of Mathematics Teaching in the Middle School.
- Shopping Mall Math
http://illuminations.nctm.org/LessonDetail.aspx?ID=U99Students participate in activities in which they develop number sense in and around the shopping mall. The first lesson in this unit is appropriate for grades 3 - 5, and the second lesson is appropriate for grades 6 - 8. Both grade-level activities deal with size and space, estimation, measurement, and applications involving percent. This unit was adapted from an article entitled "Mathematics at the Mall," written by Francis Fennell, which appeared in Teaching Children Mathematics, January, 1998, vol.4, no.5, pp. 268 - 274.
- Shops at the Mall
http://illuminations.nctm.org/LessonDetail.aspx?ID=L266Students participate in an activity in which they develop number sense in and around the shopping mall. They solve problems involving percent and scale drawings.
- Too Big or Too Small?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L252In this lesson, students develop number sense through a series of three hands-on activities. Students explore the following concepts: the magnitude of a million, fractions between 0 and 1, and the effect of decimal operations.
- Volt Meter
http://illuminations.nctm.org/ActivityDetail.aspx?ID=152This student interactive, from an Illuminations lesson, allows students to learn about positive and negative numbers by exploring the voltage of batteries.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6